Abstract: The singing frequency ( pitch) is an important criterion for measuring the singer's singing ability.

The“tone deafness”is the phenomenon that a singer's singing frequencies are higher or lower than the music frequencies.

Based on the spectrum analysis the relative deviation of the frequency is quantitated determined. With the

randomly collected cappella records as the research object，the relative deviation of the frequency approximately follow

a normal distribution with mean 0 and standard deviation 0.03507. Thus，it is possible to define the“musical

expression deviation”for each singer by providing scores of singing precision and to propose a feasible algorithm in　evaluations of amusia.

Key words: spectrum analysis, tone deafness, amusia, statistical rule, machine learning